{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T20:25:17Z","timestamp":1745612717242},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,1,11]],"date-time":"2007-01-11T00:00:00Z","timestamp":1168473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2007,1,11]],"date-time":"2007-01-11T00:00:00Z","timestamp":1168473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2007,6]]},"DOI":"10.1007\/s00186-006-0125-x","type":"journal-article","created":{"date-parts":[[2007,1,10]],"date-time":"2007-01-10T12:22:54Z","timestamp":1168431774000},"page":"417-444","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A general approach for studying duality in multiobjective optimization"],"prefix":"10.1007","volume":"65","author":[{"given":"Radu Ioan","family":"Bo\u0163","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sorin-Mihai","family":"Grad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gert","family":"Wanka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,1,11]]},"reference":[{"key":"125_CR1","unstructured":"Bo\u0163 RI, Grad S-M, Wanka G (2004) A new constraint qualification and conjugate duality for composed convex optimization problems. Preprint 2004-15, Fakult\u00e4t f\u00fcr Mathematik, Technische Universit\u00e4t Chemnitz. J Optim Theory Appl (preprint)"},{"key":"125_CR2","doi-asserted-by":"crossref","unstructured":"Bo\u0163 RI, Grad S-M, Wanka G (2006) Fenchel\u2013Lagrange versus geometric programming in convex optimization. J Optim Theory Appl 129","DOI":"10.1007\/s10957-006-9047-2"},{"issue":"3","key":"125_CR3","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1080\/02331930410001715514","volume":"53","author":"RI Bo\u0163","year":"2004a","unstructured":"Bo\u0163 RI, Wanka G (2004a) An analysis of some dual problems in multiobjective optimization I. Optimization 53(3):281\u2013300","journal-title":"Optimization"},{"issue":"3","key":"125_CR4","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1080\/02331930410001715523","volume":"53","author":"RI Bo\u0163","year":"2004b","unstructured":"Bo\u0163 RI, Wanka G (2004b) An analysis of some dual problems in multiobjective optimization II. Optimization 53(3):301\u2013324","journal-title":"Optimization"},{"issue":"2","key":"125_CR5","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1016\/j.jmaa.2005.06.067","volume":"315","author":"RI Bo\u0163","year":"2006","unstructured":"Bo\u0163 RI, Wanka G (2006) Duality for multiobjective optimization problems with convex objective functions and D.C. constraints. J Math Anal Appl 315(2):526\u2013543","journal-title":"J Math Anal Appl"},{"issue":"2","key":"125_CR6","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s10107-002-0303-4","volume":"93","author":"E Carrizosa","year":"2002","unstructured":"Carrizosa E, Fliege J (2002) Generalized goal programming: polynomial methods and applications. Math Program 93(2):281\u2013303","journal-title":"Math Program"},{"issue":"1","key":"125_CR7","first-page":"1","volume":"5","author":"V Chankong","year":"1983","unstructured":"Chankong V, Haimes YY (1983) Optimization-based methods for multiobjective decision-making: an overview. Large Scale Syst 5(1):1\u201333","journal-title":"Large Scale Syst"},{"key":"125_CR8","unstructured":"Fliege J (2001) Approximation techniques for the set of efficient points. Habilitationsschrift, Fachbereich Mathematik, Universit\u00e4t Dortmund"},{"key":"125_CR9","unstructured":"Fliege J, Heseler A (2002) Constructing approximations to the efficient set of convex quadratic multiobjective problems. Ergebnisberichte Angewandte Mathematik, vol. 211, Fachbereich Mathematik, Universit\u00e4t Dortmund"},{"issue":"2","key":"125_CR10","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1023\/A:1021780423989","volume":"102","author":"JBG Frenk","year":"1999","unstructured":"Frenk JBG, Kassay G (1999) On classes of generalized convex functions, Gordan-Farkas type theorems and Lagrangian duality. J Optim Theory Appl 102(2):315\u2013343","journal-title":"J Optim Theory Appl"},{"issue":"3","key":"125_CR11","first-page":"357","volume":"25","author":"C Gerstewitz","year":"1983","unstructured":"Gerstewitz C (1983) Nichtkonvexe Dualit\u00e4t in der Vektoroptimierung. Wissenschaftliche Zeitschrift den Technischen Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg 25(3):357\u2013364","journal-title":"Wissenschaftliche Zeitschrift den Technischen Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg"},{"key":"125_CR12","unstructured":"Gerstewitz C, Iwanow E (1985) Dualit\u00e4t f\u00fcr nichtkonvexe Vektoroptimierungsprobleme. In: Workshop on vector optimization (Plauen, 1984), Wissenschaftliche Zeitschrift der Technischen Hochschule Ilmenau 31(2):61\u201381"},{"issue":"2","key":"125_CR13","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00940478","volume":"67","author":"C Gerth","year":"1990","unstructured":"Gerth C, Weidner P (1990) Nonconvex separation theorems and some applications in vector optimization. J Optim Theory and Appl 67(2):297\u2013320","journal-title":"J Optim Theory and Appl"},{"issue":"4","key":"125_CR14","doi-asserted-by":"crossref","first-page":"377","DOI":"10.4171\/ZAA\/205","volume":"5","author":"A G\u00f6pfert","year":"1986","unstructured":"G\u00f6pfert A, Gerth C (1986) \u00dcber die Skalarisierung und Dualisierung von Vektoroptimierungsproblemen. Z Anal Anwendungen 5(4):377\u2013384","journal-title":"Z Anal Anwendungen"},{"key":"125_CR15","unstructured":"Helbig S (1989) A scalarization for vector optimization problems in locally convex spaces. In: Proceedings of the annual scientific meeting of the GAMM (Vienna, 1988), Z Angew Math Mech 69(4):T89\u2013T91"},{"key":"125_CR16","volume-title":"Convex analysis and minimization algorithms, I and II","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty J-B, Lemar\u00e9chal C (1993) Convex analysis and minimization algorithms, I and II. Springer, Berlin Heidelberg New York"},{"issue":"2","key":"125_CR17","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/BF02592221","volume":"29","author":"J Jahn","year":"1984","unstructured":"Jahn J (1984) Scalarization in vector optimization. Math Program 29(2):203\u2013218","journal-title":"Math Program"},{"key":"125_CR18","volume-title":"Vector optimization-theory, applications, and extensions","author":"J Jahn","year":"2004","unstructured":"Jahn J (2004) Vector optimization-theory, applications, and extensions. Springer, Berlin Heidelberg New York"},{"issue":"3","key":"125_CR19","first-page":"117","volume":"11","author":"I Kaliszewski","year":"1986","unstructured":"Kaliszewski I (1986) Norm scalarization and proper efficiency in vector optimization. Found Control Eng 11(3):117\u2013131","journal-title":"Found Control Eng"},{"issue":"3","key":"125_CR20","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1137\/0331029","volume":"31","author":"PQ Kh\u00e1nh","year":"1993","unstructured":"Kh\u00e1nh PQ (1993) Optimality conditions via norm scalarization in vector optimization. SIAM J Control Optim 31(3):646\u2013658","journal-title":"SIAM J Control Optim"},{"key":"125_CR21","volume-title":"Theory of vector optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319","author":"DT Luc","year":"1989","unstructured":"Luc DT (1989) Theory of vector optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, Berlin Heidelberg New York"},{"issue":"4","key":"125_CR22","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1137\/040603097","volume":"15","author":"DT Luc","year":"2005","unstructured":"Luc DT, Phong TQ, Volle M (2005) Scalarizing functions for generating the weakly efficient solution set in convex multiobjective problems. SIAM J Optim 15(4):987\u20131001","journal-title":"SIAM J Optim"},{"key":"125_CR23","doi-asserted-by":"crossref","unstructured":"Mbunga P (2003) Structural stability of vector optimization problems. Optimization and optimal control (Ulaanbaatar, 2002), Series on Computers and Operations Research, vol. 1. World Scientific Publishing, River Edge, pp 175\u2013183","DOI":"10.1142\/9789812775368_0012"},{"issue":"3","key":"125_CR24","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1023\/A:1016031214488","volume":"114","author":"E Miglierina","year":"2002","unstructured":"Miglierina E, Molho E (2002) Scalarization and stability in vector optimization. J Optim Theory and Appl 114(3):657\u2013670","journal-title":"J Optim Theory and Appl"},{"issue":"3","key":"125_CR25","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1002\/(SICI)1099-1360(199705)6:3<131::AID-MCDA129>3.0.CO;2-S","volume":"6","author":"K Mitani","year":"1997","unstructured":"Mitani K, Nakayama HA (1997) A multiobjective diet planning support system using the satisficing trade-off method. J Multi-Criteria Decis Anal 6(3):131\u2013139","journal-title":"J Multi-Criteria Decis Anal"},{"key":"125_CR26","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton"},{"issue":"4","key":"125_CR27","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1023\/B:JOGO.0000047914.22567.66","volume":"29","author":"AM Rubinov","year":"2004","unstructured":"Rubinov AM, Gasimov RN (2004) Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation. J Global Optim 29(4): 455\u2013477","journal-title":"J Global Optim"},{"key":"125_CR28","unstructured":"Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization. Mathematics in Science and Engineering, vol 176. Academic Press, Orlando"},{"issue":"7","key":"125_CR29","first-page":"925","volume":"44","author":"B Schandl","year":"2002","unstructured":"Schandl B, Klamroth K, Wiecek MM (2002) Norm-based approximation in multicriteria programming. Global optimization, control, and games IV, Comput Math Appl 44(7):925\u2013942","journal-title":"Global optimization, control, and games IV, Comput Math Appl"},{"key":"125_CR30","unstructured":"Tammer C (1996) A variational principle and applications for vectorial control approximation problems. Preprint 96-09, Reports on Optimization and Stochastics, Martin-Luther-Universit\u00e4t Halle-Wittenberg"},{"key":"125_CR31","doi-asserted-by":"crossref","unstructured":"Tammer C, G\u00f6pfert A (2002) Theory of vector optimization. In: Ehrgott M, Gandibleux X (eds) Multiple criteria optimization: state of the art annotated bibliographic surveys. International Series in Operations Research and Management Science, vol. 52. Kluwer, Boston, pp 1\u201370","DOI":"10.1007\/0-306-48107-3_1"},{"issue":"3","key":"125_CR32","first-page":"365","volume":"4","author":"C Tammer","year":"2003","unstructured":"Tammer C, Winkler K (2003) A new scalarization approach and applications in multicriteria D.C. optimization. J Nonlinear Convex Anal 4(3):365\u2013380","journal-title":"J Nonlinear Convex Anal"},{"key":"125_CR33","doi-asserted-by":"crossref","unstructured":"Tanino T, Kuk H (2002) Nonlinear multiobjective programming. In: Ehrgott M, Gandibleux X (eds) Multiple criteria optimization: state of the art annotated bibliographic surveys. International Series in Operations Research and Management Science, vol. 52. Kluwer, Boston, pp 71\u2013128","DOI":"10.1007\/0-306-48107-3_2"},{"issue":"1","key":"125_CR34","first-page":"41","volume":"3","author":"G Wanka","year":"2001","unstructured":"Wanka G, Bo\u0163 RI (2001) A new duality approach for multiobjective convex optimization problems. J Nonlinear Convex Anal 3(1):41\u201357","journal-title":"J Nonlinear Convex Anal"},{"issue":"3","key":"125_CR35","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s001860000104","volume":"53","author":"G Wanka","year":"2000","unstructured":"Wanka G, Bo\u0163 RI (2000) Multiobjective duality for convex-linear problems II. Math Methods Oper Res 53(3):419\u2013433","journal-title":"Math Methods Oper Res"},{"issue":"3","key":"125_CR36","doi-asserted-by":"crossref","first-page":"711","DOI":"10.4171\/ZAA\/1169","volume":"22","author":"G Wanka","year":"2003","unstructured":"Wanka G, Bo\u0163 RI, Grad S-M (2003) Multiobjective duality for convex semidefinite programming problems. Z Anal Anwendungen (J Anal Appl) 22(3):711\u2013728","journal-title":"Z Anal Anwendungen (J Anal Appl)"},{"key":"125_CR37","doi-asserted-by":"crossref","unstructured":"Wanka G, Bo\u0163 RI, Vargyas ET (2006) Duality for location problems with unbounded unit balls. Eur J Oper Res DOI 10.1016\/j.ejor.2005.09.048","DOI":"10.1016\/j.ejor.2005.09.048"},{"issue":"3","key":"125_CR38","first-page":"103","volume":"36","author":"P Weidner","year":"1990","unstructured":"Weidner P (1990) An approach to different scalarizations in vector optimization. Wissenschaftliche Zeitschrift der Technischen Hochschule Ilmenau 36(3):103\u2013110","journal-title":"Wissenschaftliche Zeitschrift der Technischen Hochschule Ilmenau"},{"issue":"4","key":"125_CR39","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/BF01720318","volume":"16","author":"P Weidner","year":"1994","unstructured":"Weidner P (1994) The influence of proper efficiency on optimal solutions of scalarizing problems in multicriteria optimization. OR Spektrum 16(4):255\u2013260","journal-title":"OR Spektrum"},{"issue":"1","key":"125_CR40","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/02331937708842405","volume":"8","author":"AP Wierzbicki","year":"1977","unstructured":"Wierzbicki AP (1977) Basic properties of scalarizing functionals for multiobjective optimization. Math Operationsforsch Statist Ser Optimization 8(1):55\u201360","journal-title":"Math Operationsforsch Statist Ser Optimization"},{"key":"125_CR41","doi-asserted-by":"crossref","unstructured":"Winkler K (2003) Skalarisierung mehrkriterieller Optimierungsprobleme mittels schiefer Normen. In: Habenicht W, Scheubrein B, Scheubein R (eds) Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis. Deutscher Universit\u00e4ts-Verlag, Wiesbaden, pp 173\u2013190","DOI":"10.1007\/978-3-322-81539-2_9"},{"issue":"3","key":"125_CR42","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1137\/S0363012902411532","volume":"42","author":"A Zaffaroni","year":"2003","unstructured":"Zaffaroni A (2003) Degrees of efficiency and degrees of minimality. SIAM J Control Optim 42(3):1071\u20131086","journal-title":"SIAM J Control Optim"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-006-0125-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00186-006-0125-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-006-0125-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-006-0125-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T23:09:41Z","timestamp":1652828981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00186-006-0125-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,11]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["125"],"URL":"https:\/\/doi.org\/10.1007\/s00186-006-0125-x","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1,11]]},"assertion":[{"value":"16 October 2006","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2006","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2007","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}